Question

solve
|2x - 3| = 6
x =
(simplify your answers. type an integer or a fraction. use a comma to separate answers as needed.)

Explanation:

Step1: Recall absolute value definition

If \(|A| = B\) (\(B\geq0\)), then \(A = B\) or \(A=-B\). For \(|2x - 3|=6\), we have two cases.

Step2: Solve Case 1: \(2x - 3 = 6\)

Add 3 to both sides: \(2x=6 + 3=9\).
Divide by 2: \(x=\frac{9}{2}\).

Step3: Solve Case 2: \(2x - 3=-6\)

Add 3 to both sides: \(2x=-6 + 3=-3\).
Divide by 2: \(x=-\frac{3}{2}\).

Answer:

\(x=\frac{9}{2},-\frac{3}{2}\) (or \(4.5, - 1.5\))